Factor 4k^2+12k+9

$4 k^{2} + 12 k + 9$

Step 1

Rewrite $4 k^{2}$ as ${(2 k)}^{2}$ .

${(2 k)}^{2} + 12 k + 9$

Step 2

Rewrite $9$ as $3^{2}$ .

${(2 k)}^{2} + 12 k + 3^{2}$

Step 3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$12 k = 2 \cdot (2 k) \cdot 3$

Step 4

Rewrite the polynomial.

${(2 k)}^{2} + 2 \cdot (2 k) \cdot 3 + 3^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 2 k$ and $b = 3$ .

${(2 k + 3)}^{2}$